相关论文: Finite speed of propagation for a non-local porous…
We study a porous medium equation with fractional potential pressure: $$ \partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u, $$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. To be specific, the problem is posed for $x\in…
We study a porous medium equation with fractional potential pressure: $$ \partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u, $$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. The problem is posed for $x\in \mathbb{R}^N$, $N\geq…
We prove finite speed of propagation for the multiplicative stochastic wave equation in two and three dimensions which leads us to a global space-time well-posedness result for the cubic nonlinear equation in the analogue of the energy…
We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove…
Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical…
We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free…
We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy…
In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in $\mathbb{R}^d$. The nonlocal operator we…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in…
It is shown that the dispersion and attenuation functions in a linear viscoelastic medium with a positive relaxation spectrum have a sublinear growth rate at very high frequencies. A local dispersion relation in parametric form is found.…
Finite speed of propagation is established for non-negative weak solutions to a thin film approximation of the two-phase Muskat problem. The temporal expansion rate of the support matches the scale invariance of the system. Moreover, we…
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for non-local delayed reaction-diffusion equation.
We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation $u_t = u_{xx} + f(u)$ with $f(0)=f(1)=0$, and $f>0$ in $(0,1)$, which permits, in principle, the calculation of the exact speed for…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The proof uses energy methods, which are adaptions of…
We propose some modification of Maxwell's equations describing mediums which electric and magnetic properties are changed essentially after interaction with outer electromagnetic field. We show for such mediums that electromagnetic waves…
We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.
In the slow diffusion case unbounded supersolutions of the porous medium equation are of two totally different types, depending on whether the pressure is locally integrable or not. This criterion and its consequences are discussed.
In this paper, we prove the existence of the spreading speed of nonlocal KPP equations in two cases: 1. The media is almost periodic and the kernel of diffusion is continuous; 2. The media is periodic and the diffusion is not continuous but…